Signal enhancement and noise reduction is usually accomplished through data smoothing if the intrinsic signal shape is not distorted in the smoothing process. Excessive smoothing, however, can actually reduce the signal-to-noise ratio. In logging data, a compromise must be made between noise reduction and the preservation of the vertical detail intrinsic to the sensor. Because the vertical resolution of nuclear tools is typically around one foot smoothing filters wider than this results in a loss of vertical detail. The current practice is to sample at half foot intervals with either a three point rectangular or triangular running average filter of the raw data. Increasingly, finer sampling is being employed. Service companies using finer sampling rates, such as 0.1', must use spatial filters wider than the sample period to reduce the log noise.
It is important to distinguish between two related but distinct concepts, namely, data smoothing and deconvolution. The object of data smoothing is to reduce noise and enhance the signal, but this may reduce the vertical detail. In contrast, deconvolution enhances vertical detail but results in increased noise, see A. M. Morland, "Special log processing for thin zones using geological impulse response functions, with particular application to total and spectral gamma ray logs," The Log Analyst, vol. 25, no. 76, p. 23, 1984. Several publications addressing the deconvolution problem introduced external information to achieve both vertical sharpening and noise reduction. For example,. see J. A. Czubek, "Quantitative interpretation of .gamma.-ray log in presence of random noise", presented at the SPWLA 27th Annual Logging Symposium, on Jun. 9-13, 1986, Houston, Tex. Paper KKK. Also, W. D. Lyle and D. M. Williams, "Deconvolution of well log data--an innovations approach", The log Analyst, vol. 28, no. 3, p.i. 32, 1987. Another is C. J. Dyos, "Inversion of well log data by the method of maximum entropy", presented at the 10th European Formation Evaluation Symposium, on Apr. 22-15, 1986, Aberdeen, Scotland, Paper H. P. Shen, B. White, B. Nair and S. Kerford, "Bayesian deconvolution of .gamma.-ray logs", Geophysics, vol. 52, no. 11, p. 1535, 1987. These techniques are computationally intensive and are applied after logging. The difficulty and extensive nature of data conversion by excessive computation inherently prevents the provision of realtime output. By contrast, the present disclosure is directed to a system which is markedly simple in comparison and is therefore able to provide an output which is substantially in realtime. That is, data is recorded continuously as the tool moves up the borehole, typically taking readings at designated intervals along the borehole, data is output as rapidly as sufficient data vertically of the borehole is obtained. In part, this depends on the spacing of data points along the borehole. The present system, however, is very useful in obtaining data with close spacing, even as close as 0.1 foot. To avoid a computationally intensive procedure like deconvolution, some procedures employ secondary data from intrinsically sharper devices to enhance the vertical details. See for example J. E. Galford, C. Flaum, W. A. Gilchrist, Jr., and S. W. Duckett, "Enhanced resolution processing of compensated neutron logs:, presented at the 61st Annual Technical Conference and Exhibition of SPE, on Oct. 5-8, 1986, New Orleans, LA, Paper 15541. C. Flaum, J. E. Galford and A. Hastings, "enhanced vertical resolution processing of dual detector gamma-gamma density logs", presented at the SPWLA 28th Annual Logging Symposium, on Jun. 29-Jul. 2, 1987, London, England, Paper M. The Flaum article may also relate to the procedure disclosed in U.S. Pat. No. 4,786,796 which involves matched sensor signals in a dual detector system.
Realtime data smoothing must rely on computationally efficient (and therefore mathematically simple) methods to achieve good noise reduction without a serious loss of vertical detail, such as described by W. E. Schultz and S. G. Thadani, "Applications of digital filtering techniques to nuclear well logs", presented at the SPWLA 22nd Annual Logging Symposium, on Jun. 23-26, 1981, Mexico City, Mexico, Paper UU. Adaptive filters were developed to recognize the logging data where signal level is substantially constant with depth and provide extra smoothing in these regions; see, for example, G. L. Mathis, "Smoothing spectral gamma logs: A simple but effective technique", Geophysics, vol. 52, no. 3, p. 363, 1987. There are also filters designed with information from other logs to assist in recognizing bed boundaries. Unfortunately, these techniques are still more computationally intensive than simple filtering since filtering coefficients must be frequently recomputed. Digital filters formed of n serially connected stages typically involve c.sub.n coefficients which must be calculated on each discrete input, or perhaps in a compromise to reduce computation, such c.sub.n coefficients must be recalculated at least periodically if not on every data input.
A previously reported iterative smoothing algorithm that is simple, computationally efficient and effective in preserving sharpness is described by H. C. Hayden, "Data smoothing routine", Computers in Physics, Nov/Dec 1987. Since this algorithm uses the system (impulse response) function of the sensor as a filter, the sharpness of the data is preserved to within the limits of this function while removing random noise. This filter can be applied to log data and spectral data. Simulated and real log data is presented that illuminates the characteristics of this procedure. The results reveal that only a few iterations are required to obtain satisfactory results. Furthermore, the performance is not strongly dependent on the actual shape of the system transfer function. Finally, a single pass procedure is developed which is exactly equivalent to the iterative procedure. The use of a single pass procedure remarkedly reduces the computations necessary which would otherwise be involved in a iterative procedure involving several of data. The single pass procedure thus enables substantial presentation of data in realtime. By contrast, a multiple pass iterative procedure can theoretically be accomplished in realtime, but it typically requires repeated convolution of the filter function with the data requiring a large computing capacity. This militates against the use of smaller computers in the field where the logging equipment is typically operated. It is not uncommon for the logging equipment to be required in extremely remote locations so that only portable equipment can be used. There is a limit to size even with truck-mounted portable computers. Accordingly, as a practical matter, realtime computation is made possible where a single pass technique is used as is taught in the present disclosure. Spatial filtering coefficients are computed from the system function directly so that only a single pass is required; in the case of a Gaussian system function, an analytic expression for the filter coefficients is derived.
By the implementation of a single pass system, computational requirements are markedly reduced. Moreover, precise premeasurement of the system transfer function is not such a rigid requirement. The preferred embodiment employs a Gaussian system function, whether the equivalent of one pass or several passes, because the Gaussian system transfer function can be easily calculated. As will be shown hereinafter, multiple passes through a Gaussian system function involves convolution (and inherently deconvolution) and there is an ease or simplicity obtained by resort to the Gaussian function.
The present disclosure is therefore summarized as a downhole logging system particularly adapted for use with nuclear logging devices or other logging devices which provide discrete output measurements. There is a determinable system transfer function involved in the sensor. It is typically modeled after a Gaussian transfer function so that calculation thereof is relatively straight forward. A filter which has a transfer function in accordance with the teachings of this disclosure is incorporated in the data flow path. The filter enables noise reduction and improvement of the signal to noise ratio while maintaining virtually all of the intrinsic vertical detail.